Until recently, most commercially available electrostatic quadrupole systems were constructed using metallic electrodes with circular cross-sections. Such structures were complicated to machine and the exact quadrupole field existed only in a small region in the vicinity of the center of symmetry of the structure. Moreover, since gaps existed between the electrodes, the resulting electric field was easily influenced by charges randomly accumulated on the inner surface of the enclosure for the electrode structure.
The primary desirable characteristic of an electrostatic quadrupole field (EQF) is that, in such a field, electric intensity varies linearly with the position. In an X-Y plane perpendicular to a Z-axis, the simplest expression of the potential distribution which satisfies this condition is EQU V(x,y)=E.sub.o (x.sup.2 -y.sup.2) (1)
where E.sub.o is a position independent factor which can be time dependent.
In such a field, the equipotential lines are sets of rectangular hyperbolae in the X-Y plane with a four-fold symmetry about the Z-axis. Therefore, an ideal quadrupole field would be generated by a set of four hyperbolically shaped metal rods with adjacent electrodes oppositely charged. Such a structure has been described by P. H. Dawson in "Advances in Electronics and Electron Physics" Supplement 13B, p. 173, Academic Press, 1980.
However, in actual practice, hyperbolic shapes are difficult to machine precisely and to align properly with their respective electrodes. Therefore, most commercial quadrupole systems are made using metallic rods of circular cross-sections. Such systems are used as an approximate substitute for the hyperbolic shapes. This so-called "four rods" EQF system has been described by D. R. Denison in Journal of Vacuum Science and Technology 8, 266, 1971.
Although both the hyperbolic and four rod structures have been widely used in the prior art, each structure has serious disadvantages. Since the hyperbolic or circular rods are both convex, the space which they occupy is much greater than the working space. In particular, with respect to the four circular rod structure, only a quasi-hyperbolic field and not an "exact" EQF can be produced. Therefore, the field is effective only in a limited region near the center of symmetry. Thus, only when x and y are small, does the potential distribution in such a system approximately satisfy the relationship set forth in Eq. (1). The field will deviate substantially from Eq. (1) as x or y increase. If a circular tube is used as an enclosure for such an electrode structure, the ratio of working area radius to tube radius is usually less than 1:4. Moreover, as the electrodes are separated by substantial gaps, any resulting electric field will be influenced by charges randomly accumulated on the inner surface of the enclosure for the electrodes, which is usually made of glass or ceramics.